Sam Sloan [mailto:samhsloan@gmail.com] is age 71. His company, Ishi Press, has published or reprinted 380 books including 140 chess books and books on go, bridge, solitaire and 10x10 draughts. He knew Ken Grover as a chess player. Will you most knowledgeable folks jump in and answer some or all of his questions? Your words might end up in his book. Here are the questions he sent me today by e-mail:

"I am planning to reprint a book on checkers by Fred Reinfeld. I want to include a section on where to play and on the American Checkers Federation. How to join. Who are the best players? Is the game in decline or are there strong up coming players? Is it true that the best checkers player in the world is now a computer? Has the game been solved?"

Bill, I really enjoyed Sam Sloan's reprint of First Book Of Chess by I.A. Horowitz and Fred Reinfeld. I hope Sam Sloan goes through with his planto reprint Fred Reinfeld's checker book. Some important background information may be found in Bob Newell's introduction to How To Win At Checkers from the Checker Maven PDF reprint:

The tabs from the above home page have much information on the ACF and checkers. From ACF Home Page > ACF Info tab>Join the ACF, shows how to join the ACF.From ACF Home Page>Tournaments tab>Announcements, shows where to play in upcoming events, month by month.

As is generally considered in chess, the strongest checker player in the world is probably a computer.The official Man vs Machine World Champion is Chinook, the computer program that beat Don Lafferty by one game with 31 draws in 1995.The 1995 match was more decisive than the default victory of Chinook when Marion Tinsley dropped out due to ill health after six drawn games in 1994.It is the 1992 match that Tinsley will forever be remembered as long a checkers is played, when he beat Chinook by 4 Wins, 2 Losses, and 33 Draws.Dr. Tinsley was the fist Man vs Machine World Champion!

Has checkers been solved? Dr. Johathan Schaeffer claimed that Chinook has solved checkers as a draw in 2007. That claim has been disputed on this ACF Forum, but my layman's impression is that Schaeffer's claim is generally accepted.The claim is for weakly solving (or ultra-weekly solving?) checkers. I look forward to the day when checkers is strongly solved.

Is checkers in decline? I am not sure, I hope not! There are strong up coming players around the world! The best male players based on who has been invited to China recently areSergio Scarpetta of Italy, Michele Borghett of Italy, Ron King of Barbados, Lubabalo Kondlo of South Africa, and last but not least Alex Moiseyev of USA. The best female players areAmangul Berdiyeva of Turkmenistan and Nadiya Chyzhevska of Ukraine.

The WCDF, World Checkers Draughts Federation, is made up of many national federations including the ACF. The WCDF conducts the World Championships and their website has much information on world checkers draughts:

No it hasn't. A group of computer scientist claimed to have weakly solved checkers a few years back by doing long searches. This is not a theorical sound way of solving checkers. It might require a computer science degree to undestand why so I won't bother with a longer description. It is like if somebody claims to have build a perpeptual motion machine this is impossible but might still be interesting if they give some kind of explanation as to how long the machine will function. To my knowledge they have not quantified exactly how far their "solution" is from being sound let alone amitted this. This makes their actions worse than simply overselling their results and closer to being a scam.

The end game of checkers on the otherhand has been solved by theoretically sound methods from 1 piece up to 10 pieces (5 per player).

I believe the term “weakly solved” is just a euphemism for “Failed, but we’re half way there”. Indeed, it was pointed out some time ago that certain positions – notably Dr. T. J. Brown’s “La Pucelle” (the virgin fortress) remain unsusceptible to computer analysis. (see Boland’s Masterpieces page 154 for this position)

To the best of my memory Chinook scientifically doesn't make the best move and theoretically some wins can be missing. From my prospective - this cannot be call "solve" in any way ... either GAYP or 3 moves. The only thing program confirmed - GAYP is drawn style for both sides. People knew this more than 100 years ago.

Concerning checkers decline - YES, today checkers are on decline around the World. Welcoming several great players from Italy doesn't really change the whole picture. WCDF is extremely passive in the past several years. However, I really don't know what needs and can be done to improve things.

No, we are on the same page and I totally agree with you regarding money, sponsors and prizes. But I am old skeptic and pessimist and have serious doubts that this will be done during my life time unless some checkers player win in lottery.

While I agree Chinook is probably not "perfect" in its play, it has most definitely mathematically proved that the starting position of the game will produce a draw if both sides play perfect. That is all Schaeffer's project was intended to do. Of course, we have known this result for a long time, but it is still an accomplishment nonetheless that he created a program so powerful that it cannot lose a game. I would say checkers is solved considering the definition of the word:

solvefind an answer to, explanation for, or means of effectively dealing with (a problem or mystery).

Based on the definition, all it had to do was find the answer. Well, we knew what the answer was, but it proved the answer 100%! Proof of the solution was provided by the team on their website too, so I it certainly seems it can be trusted unless they are all somehow outright lying, which I don't believe.

You can also find some interesting rationale for solved games on wikipedia: https://en.wikipedia.org/wiki/Solved_game. According to the source, checkers has been solved on a "weak" level, but still solved nonetheless.

Lastly, what does this mean for checker players? Absolutely nothing. Humans will never come close to perfection of the game as the game tree is just way too big and complex. Checkers will always be a struggle for human players no matter how much effort anyone is to put into the game. The only problem I see is this perceived concept by non-players that checkers should just be put to the side because it has been weakly solved. So while it is evident the game has been solved, it does seem this word "solved" can be a bit misleading to some. As great of an accomplishment it is, it also hardly means anything.

Chexhero wrote:While I agree Chinook is probably not "perfect" in its play, it has most definitely mathematically proved that the starting position of the game will produce a draw if both sides play perfect.

There seems to be a confusion of two subjects:

1. The definition of solvingA position in checkers can have one of 3 game theoretic values: loss, draw or win - weakly solving means you don't know the exact value but only if a position is "loss or drawn" or "drawn or win". Weakly solving the game is not very interesting in practical terms since we already have a good idea which positions are weak. On the other hand it is still theoretically interesting this is not my main critique.

2. The method of solvingComputing endgame databases is a sound way of resolving the game theoretical value of all the subset of positions with a limited number of pieces. You can only do this with a limited number of pieces because after you add enough pieces there are simply too many positions. Searching is an imperfect way of evaluating a position/selecting a move where you apply moves up to a level e.g 2 then 4,6,8,10,12,14,16,18,20,22 etc imperfectly evaluate the leaf positions and choose the optimal position to end up in given that your opponent will also try to achieve the optimal leaf position. A search tree is formed where there from the start position are 7 difference choices (11-15, 11-16 etc) that each have a branch and for each of these branches for instance 11-15 you can go 23-19 or 22-17 etc which create more branches. This creates what is called a combinatorial explosion (https://en.wikipedia.org/wiki/Combinatorial_explosion). You can stop the search in case one player is out of pieces/moves or you have so few pieces that you can look up the game theoretic value in an endgame database.

In checkers we have this concept called seesawing which means that starting a search will never end because you will never reach a position where you can resolve the position - the search tree is infinite hence my analogy with the perpetual motion machine - we know this is impossible! You can to a certain extend try to detect repetitions and the 40 move rule could also be used to mitigate the situation but all in all there are simply too many combinations so in practice the search tree is infinite. I am absolutely certain that the Chinook team cuts off lines of the search tree - thus making their "proof" invalid. I am basing this on my understanding of the combinatorial explosion and the fact that they wrote on their homepage after the first couple of openings were "solved" that they had modified how far they search ie they are cutting off lines. The fortress positions are excellent examples of why this matters.

On top of this many used search techniques are imperfect but are used anyway because they help you to search to a deeper level which in the end will give you a more precise value - this is done because it is accepted that searching is what we call a heuristical approarch (ie imperfect) so in that context it makes sense. The exact nature of these techniques is too complicated to go into detail here but If you were to use searching for solving you would have to stop using these techniques which would worsen the combinatorial explosion and ensure that you are not able to search very far. Some of these techniques (for instance the technique call zobrist keys) fail extremely rarely so you could argue that it is too unlikely to matter. An analogy here could be that if you play the lottery once you can ignore the chance of you winning the top price - if you play the lottery a million times the chance improves somewhat.

So in terms of a Chinook establishing a mathematical proof - you can "prove" anything as long as you start from an incorrect axiom but they definitely in no way have solved checkers.

I would argue that the program doesn't need to reach every possible position on the game tree because it can force the opposition into a position that it knows will draw. In other words, the program can always manage to avoid the uncertainties of a fortress position or seesaw situations. To me, all "solves" really means is that the program can prove that it can force a draw no matter what is played against it. It absolutely doesn't mean it can accurately solve every single position on the board. Some positions just aren't necessary because it can avoid them and I would think this is why certain lines were probably cut off the search tree.

If indeed you and others are certain checkers has not been at least weakly solved, then perhaps we should challenge Schaeffer and his team on their conclusions. Claiming that their 20 year project result was actually just a scam is a pretty bold statement. While I can't actually prove their "proof", I am more inclined to believe what they are saying, but then again maybe I am just too trusting.

Chexhero wrote:I would argue that the program doesn't need to reach every possible position on the game tree because it can force the opposition into a position that it knows will draw. In other words, the program can always manage to avoid the uncertainties of a fortress position or seesaw situations. To me, all "solves" really means is that the program can prove that it can force a draw no matter what is played against it. It absolutely doesn't mean it can accurately solve every single position on the board. Some positions just aren't necessary because it can avoid them and I would think this is why certain lines were probably cut off the search tree.

Yes if only you could pick and choose you opponents moves when you play checkers real life .

If indeed you and others are certain checkers has not been at least weakly solved, then perhaps we should challenge Schaeffer and his team on their conclusions. Claiming that their 20 year project result was actually just a scam is a pretty bold statement. While I can't actually prove their "proof", I am more inclined to believe what they are saying, but then again maybe I am just too trusting.

The reason why I use that term is that I KNOW that the method they used is not sound and I find it infuriating that they haven't openly laid their cards on the table admitted that it isn't 100% sound and given some kind of notion how far away it is from being sound. I have a university degree in computer science and have made my own (still unpublished) checkers program so I have a relatively deep undestanding of the subject. As a service I have attempted to explain why but is it a complicated topic. I don't blame you for trusting them more than me - they certainly have the whole world fooled.